find the length of major axis minor axis length of latest rectum and eccentricity of following ellipse 9x^2 +4y^2=36
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The given is the ellipse x²/36 + y²/16 = 1.
Here,
The denominator of x²/36 is greater than the denominator of y²/16
Therefore,
the major axis is along the x - axis.
the minor axis is along the y - axis.
On comparing the given equation with x²/a² + y²/b² = 1
We obtain
a = 6 and b = 4
=> c = √a² - b²
= √(6)² - (4)²
= √36 - 16
= √20
= 2√5
Therefore,
The coordinates of the fouc are (2√5, 0) and (-2√5, 0)
The coordinates of the vertices are (6, 0) and (-6, 0).
Length of majar axis => 2a = 2 × 6 = 12
Length of minor axis => 2b = 2 × 4 = 8
Eccentricity , e = c/a
=> 2√5/6
=> √5/3
Length of Latus rectum => 2b²/a
=> 2 × 16/6
=> 16/3
Hence, the coordinates of the fouc are (2√5, 0) and (-2√5, 0), The coordinates of the vertices are (6, 0) and (-6, 0). Length of majar axis = 12. Length of minor axis = 8, Eccentricity = √5/3, And Length of Latus rectum = 16/3.
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